...and their mother's, mother, etc. In other words, a person is a matrilineal descendant of a person -if- their mother's, mother's, mother's, mother, etc was the person.
Let's put it this way. Write down your name. Put your mother's name under it. Then write -her- mother's name down, and then -her- mother, and go back as far as you can. That's your mitochondrial lineage--and you have only one such lineage. You have a piece of DNA that looks -exactly- like that of the last person you listed.
Men can test too. They just don't pass that piece of DNA down. It -always- comes from the mother.